A fixed point iteration method using Green's functions for the solution of nonlinear boundary value problems over semi-Infinite intervals

References

• S. Abbasbandy and E. Shivanian, Multiple solutions of mixed convection in a porous medium on semi–infinite interval using pseudo–spectral collocation method, Commun. Nonlinear Sci. Numer. Simulat. 16 (2011), pp. 2745–2752.
   Web of Science ®Google Scholar
• R.P. Agarwal and D. O'Regan, Singular problems on the infinite interval modelling phenomena in draining flows, IMA J. Appl. Math. 66(6) (2001), pp. 621–635.
   Web of Science ®Google Scholar
• R.P. Agarwal and D. O'Regan, Infinite interval problems modeling the flow of a gas through a semiinfinite porous medium, Stud. Appl. Math. 108(3) (2002), pp. 245–257.
   Web of Science ®Google Scholar
• R.P. Agarwal and D. O'Regan, Infinite interval problems modeling phenomena which arise in the theory of plasma and electrical potential theory, Stud. Appl. Math. 111(3) (2003a), pp. 339–358.
   Web of Science ®Google Scholar
• R.P. Agarwal and D. O'Regan, Infinite interval problems arising in non-linear mechanics and non- Newtonian fluid flows, Int. J. Non–Linear Mech. 38(9) (2003b), pp. 1369–1376.
   Web of Science ®Google Scholar
• R.P. Agarwal and D. O'Regan, An infinite interval problem arising in circularly symmetric deformations of shallow membrane caps, Int. J. Non–Linear Mech. 39(5) (2004), pp. 779–784.
   Web of Science ®Google Scholar
• V. Berinde, Iterative approximation of fixed points, Lecture Notes in Mathematics, Springer, 2007.
   Google Scholar
• W.J. Beyn, Numerical methods for dynamical systems, in Advances in Numerical Analysis, W. Light, ed., Clarendon Press, Oxford, 1992, pp. 175–236.
   Google Scholar
• J.P. Boyd, The optimization of convergence for Chebyshev polynomial methods in an unbounded domain, J. Comput. Phys. 45(1) (1982), pp. 43–79.
   Web of Science ®Google Scholar
• J.P. Boyd, Spectral methods using rational basis functions on an infinite interval, J. Comput. Phys. 69(1) (1987a), pp. 112–142.
   Web of Science ®Google Scholar
• J.P. Boyd, Orthogonal rational functions on a semi-infinite interval, J. Comput. Phys. 70(1) (1987b), pp. 63–88.
   Web of Science ®Google Scholar
• J.P. Boyd, Padé approximant algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain, Comput. Phys. 11(3) (1997), pp. 299–303.
   Google Scholar
• J.P. Boyd, C. Rangan and P.H. Bucksbaum, Pseudospectral methods on a semi-infinite interval with application to the hydrogen atom: A comparison of the mapped Fourier-sine method with Laguerre series and rational Chebyshev expansions, J. Comput. Phys. 188(1) (2003), pp. 56–74.
   Web of Science ®Google Scholar
• M. Countryman and R. Kannan, Nonlinear boundary value problems on semi-infinite intervals, Comput. Math. Appl. 28(10–12) (1994), pp. 59–75.
   Web of Science ®Google Scholar
• F.R. De Hoog and R. Weiss, An approximation theory for boundary value problems on infinite intervals, Computing 24 (1980), pp. 227–239.
   Web of Science ®Google Scholar
• R. Fazio, A novel approach to the numerical solution of boundary value problems on infinite intervals, SIAM J. Numer. Anal. 33(4) (1996), pp. 1473–1483.
   Web of Science ®Google Scholar
• R. Fazio, A survey on free boundary identification of the truncated boundary in numerical BVPs on infinite intervals, J. Comput. Appl. Math. 140(1–2) (2002), pp. 331–344.
   Web of Science ®Google Scholar
• R. Fazio, A free boundary approach and Keller's box scheme for BVPs on infinite intervals, Int. J. Comput. Math. 80 (2003), pp. 1549–1560.
   Web of Science ®Google Scholar
• R. Fazio and A. Jannelli, Finite difference schemes on quasi-uniform grids for BVPs on infinite intervals, J. Comput. Appl. Math. 269 (2014), pp. 14–23.
   Web of Science ®Google Scholar
• R. Fazio and A. Jannelli, BVPs on infinite intervals: A test problem, a nonstandard finite difference scheme and a posteriori error estimator, Math. Meth. Appl. Sci. 40(18) (2017), pp. 6285–6294.
   Web of Science ®Google Scholar
• R. Fazio and A. Jannelli, Numerical study on gas flow through a micro-nano porous medium based on finite difference schemes on quasi-uniform grids, Int. J. Non–Linear Mech. 105 (2018), pp. 186191.
   Web of Science ®Google Scholar
• D. Funaro and O. Kavian, Approximation of some diffusion evolution equations in unbounded domains by Hermite functions, Math. Comput. 57(196) (1991), pp. 597–619.
   Web of Science ®Google Scholar
• I.P. Gavrilyuk, M. Hermann, M.V. Kutnivc and V.L. Makarovd, Adaptive algorithms based on exact difference schemes for nonlinear BVPs on the half-axis, Appl. Numer. Math. 59 (2009), pp. 1529–1536.
   Web of Science ®Google Scholar
• A. Granas, R.B. Guenther, J.W. Lee and D. O'Regan, Boundary value problems on infinite intervals and semiconductor devices, J. Math. Anal. Appl. 116(2) (1986), pp. 335–348.
   Web of Science ®Google Scholar
• C.E. Grosch and S.A. Orszag, Numerical solution of problems in unbounded regions: Coordinate transforms, J. Comput. Phys. 25(3) (1977), pp. 273–295.
   Web of Science ®Google Scholar
• B.-Y. Guo, Gegenbauer approximation and its applications to differential equations on the whole line, J. Math. Anal. Appl. 226(1) (1998), pp. 180–206.
   Web of Science ®Google Scholar
• B.-Y. Guo, Jacobi spectral approximations to differential equations on the half line, J. Comput. Math. 18(1) (2000), pp. 95–112.
   Web of Science ®Google Scholar
• B.-Y. Guo, J. Shen and Z.-Q. Wang, A rational approximation and its applications to differential equations on the half line, J. Sci. Comput. 15(2) (2000), pp. 117–147.
   Google Scholar
• I. Hashim and S.K. Wilson, The onset of oscillatory Marangoni convection in a semi-infinitely deep layer of fluid, Z. Angew. Math. Phys. 50(4) (1999), pp. 546–558.
   Web of Science ®Google Scholar
• H. Ibdah, S.A. Khuri and A. Sayfy, Two-point boundary-value problems over a semi-infinite domain: A coupled ABC and spline collocation approach, Int. J. Comput. Methods Eng. Sci. Mech. 15(5) (2014), pp. 448–456.
   Google Scholar
• H.Q. Kafri and S.A. Khuri, Bratu's problem: A novel approach using fixed–point iterations and Green's functions, Comput. Phys. Commun. 198 (2016), pp. 97–104.
   Web of Science ®Google Scholar
• H.Q. Kafri, S.A. Khuri and A. Sayfy, A new approach based on embedding Green's functions into fixed–point iterations for highly accurate solution to Troesch's problem, Int. J. Comput. Methods Eng. Sci. Mech. 17(2) (2016), pp. 93–105.
   Web of Science ®Google Scholar
• S.A. Khuri and I. Louhichi, A novel Ishikawa–Green's fixed point scheme for the solution of BVPs, Appl. Math. Lett. 82 (2018), pp. 50–57.
   Web of Science ®Google Scholar
• S.A. Khuri, A. Sayfy and A. Zaveri, A new iteration method based on Green's functions for the solution of PDEs, Int. J. Appl. Comput. Math. 3(4) (2017), pp. 3091–3103.
   Google Scholar
• R.E. Kidder, Unsteady flow of gas through a semi–infinite porous medium, J. Appl. Mech. 24 (1957), pp. 329–332.
   Google Scholar
• M. Lentini and H.B. Keller, Boundary value problems on semi–infinite intervals and their numerical solutions, SIAM. J. Numer. Anal. 17(4) (1980), pp. 577–604.
   Web of Science ®Google Scholar
• M. Maleki, I. Hashim and S. Abbasbandy, Analysis of IVPs and BVPs on semi-infinite domains via collocation methods, J. Appl. Math. 2012 (2012), Article ID 696574, 21 pages.
   Web of Science ®Google Scholar
• P.A. Markowich, A theory for the approximation of solution of boundary value problems on infinite intervals, SIAM J. Math. Anal. 13 (1982), pp. 484–513.
   Web of Science ®Google Scholar
• P.A. Markowich, Analysis of boundary value problems on infinite intervals, SIAM J. Math. Anal. 14 (1983), pp. 11–37.
   Web of Science ®Google Scholar
• A.S.V. Ravi Kanth and Y.N. Reddy, A numerical method for solving two-point boundary value problems over infinite intervals, Appl. Math. Comput. 144(2–3) (2003), pp. 483–494.
   Web of Science ®Google Scholar
• T.N. Robertson, The linear two point boundary value problems on an infinite interval, Math. Comput. 25 (1971), pp. 475–483.
   Web of Science ®Google Scholar
• J. Shen, Stable and efficient spectral methods in unbounded domains using Laguerre functions, SIAM. J. Numer. Anal. 38(4) (2000), pp. 1113–1133.
   Web of Science ®Google Scholar
• S.V. Tsynkov, Numerical solution of problems on unbounded domains. A review, Appl. Numer. Math. 27 (1998), pp. 465–532.
   Web of Science ®Google Scholar
• A.I. van de Vooren and D. Dijkstra, The Navier-Stokes solution for laminar flow past a semi-infinite flat plate, J. Eng. Math. 4 (1970), pp. 9–27.
   Web of Science ®Google Scholar